Geometric And P Adic Modular Forms Of Half Integral Weight PDF Download
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Author | : Nicholas Adam Ramsey |
Publisher | : |
Total Pages | : 112 |
Release | : 2004 |
Genre | : Forms, Modular |
ISBN | : |
Download Geometric and P-adic Modular Forms of Half-integral Weight Book in PDF, ePub and Kindle
Author | : Nancy Childress |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821851748 |
Download Arithmetic Geometry Book in PDF, ePub and Kindle
This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral weight and their roles in arithmetic geometry. The volume also contains material on the Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including p-adic L-functions and p-adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and computation of torsion groups of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations. With contributions by some of the leading experts in the field, this book provides a look at the state of the art in arithmetic geometry.
Author | : Ken Ono |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821833685 |
Download The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series Book in PDF, ePub and Kindle
Chapter 1.
Author | : Anne Schwartz |
Publisher | : |
Total Pages | : 182 |
Release | : 1989 |
Genre | : |
ISBN | : |
Download Modular Forms of Weight 1/2 on Products of P-adic Upper Half Planes Book in PDF, ePub and Kindle
Author | : Fernando Q. Gouvea |
Publisher | : Springer |
Total Pages | : 129 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540388540 |
Download Arithmetic of p-adic Modular Forms Book in PDF, ePub and Kindle
The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.
Author | : V. Vatsal |
Publisher | : American Mathematical Society |
Total Pages | : 108 |
Release | : 2023-09-27 |
Genre | : Mathematics |
ISBN | : 1470465507 |
Download Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight Book in PDF, ePub and Kindle
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Author | : Alan Adolphson |
Publisher | : Walter de Gruyter |
Total Pages | : 1150 |
Release | : 2008-08-22 |
Genre | : Mathematics |
ISBN | : 3110198134 |
Download Geometric Aspects of Dwork Theory Book in PDF, ePub and Kindle
This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.
Author | : Fabrizio Andreatta |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821836099 |
Download Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects Book in PDF, ePub and Kindle
We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.
Author | : Fritz Hörmann |
Publisher | : American Mathematical Society |
Total Pages | : 162 |
Release | : 2014-11-05 |
Genre | : Mathematics |
ISBN | : 1470419122 |
Download The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type Book in PDF, ePub and Kindle
This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.
Author | : Kathrin Bringmann |
Publisher | : American Mathematical Soc. |
Total Pages | : 409 |
Release | : 2017-12-15 |
Genre | : Mathematics |
ISBN | : 1470419440 |
Download Harmonic Maass Forms and Mock Modular Forms: Theory and Applications Book in PDF, ePub and Kindle
Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.